One of the most successful modern approaches to the study of complex biochemical reaction systems is the so-called rule-based modeling approach (via the Kappa or BioNetGen frameworks). These approaches intrinsically rely upon a sophisticated concept from theoretical computer science known as rewriting theory. The abstraction of molecules to so-called agents and of reactions to so-called rewriting rules not only permits to efficiently encode empirical information on biochemical reaction systems, but in particular permits to implement high-performance simulation algorithms as a source of “in silico” empirical data.
The central aim of the RaSiR project has been to improve upon the existing theory of rewriting systems in order to permit the development of fundamentally new approaches to algorithm design in bioinformatics. Crucially, the simulations provided by the existing rule-based modeling platforms alone are not providing sufficient information in order to understand dynamical and functional behaviors of biological systems, since the core sources of these behaviors are given by pathways and their interactions rather than individual realizations of the systems. Despite the long history of rewriting theory with over 40 years of developments, we identified certain key aspects of the theory that had previously not been considered or understood. In particular, through a close analogy to the theory of combinatorics, re-focusing the analysis of rule-based systems upon sequential compositions of rules (rather than on sequential rewriting steps) revealed a fruitful new type of mathematical structure: sequential compositions of rules have a certain associativity property, which permits to encode the non-determinism in rule compositions within a mathematical structure of so-called rule algebras.
At a fundamental level, we addressed the question of how to extrapolate from customized formulations of rewriting theories to a universal framework, accessible also to practitioners outside the bioinformatics communities. Developing this general framework permitted us to discover interesting novel application areas of rewriting theories including the stochastic dynamics of social networks, random graph models and pattern counting problems in combinatorics. Our work was motivated by the possibility of achieving a deeper understanding of the origin of functional behavior of biological systems and of their pathway dynamics, with potential applications including the discovery of potential drug targets, as well as the discovery of a variant of statistical mechanics tailor-made for the study of stochastic network models and random graphs.
